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2 angle bisectors interesect on a diagonal of ABCD, wanted and given

Source: 2020 1st Memorial Mathematical Contest "Aleksandar Blazhevski-Cane" p1

April 30, 2021
geometryconcurrencyconcurrent

Problem Statement

A convex quadrilateral ABCDABCD is given in which the bisectors of the interior angles ∠ABC\angle ABC and ∠ADC\angle ADC have a common point on the diagonal ACAC. Prove that the bisectors of the interior angles ∠BAD\angle BAD and ∠BCD\angle BCD have a common point on the diagonal BDBD.
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